The site doesn’t have any “private message” mechanism. This is very much by design. Luckily, site moderators are the one kinda-sorta exception: if you flag a post, one of your options is to send a message to a moderator. They can then initiate a private discussion with you.
That would not be the recommended solution to this situation, however.
Instead, you should learn a little bit more about who we are and what this site is about.
We don’t accept questions asking for interest in playing games here; that’s not what the site is about. We ban questions looking for groups, questions looking for GMs, and so on, too—in all cases, those just aren’t on-topic here. Questions can’t be open-ended like that, they have to be actual questions that can at least theoretically have actual answers. As in definitive, comprehensive, authoritative answers that can become a resource for future readers. Most of our site rules are geared towards encouraging these sorts of questions, and filtering out others which are better-handled on other sites. (By the way, we do have recommendations for discussion forums, which may be more interested in hosting discussions of a new game with the game’s creators.)
Links to your game are acceptable if and when it is appropriate content for an otherwise-valid question. We also expect those who are related to a product to disclaim that affiliation, just so readers know what they’re getting. And if your only reason for being here, and only content you contribute, is about your game, you might also get the cold shoulder for that.
For example, when I first joined this site, I was at the time a writer and designer for Rule of Cool, working on their game Legend. Like you, I had similar interests in getting the word out about the game. But the way I handled this was to start a meta discussion on the appropriateness of that, which is where the site agreed that the best solution was, as I said, to only allow such posts if they are legitimate content we would otherwise allow, and such affiliations are disclaimed. See wax eagle’s excellent answer, which remains the community consensus to this day:
Provided that asking/answering questions about Legend is not your only reason for being involved here, and is not the only contribution you are making. I think this is fine.
What I would advise is that you disclose your connection to Legend, probably at least in your answers.
Lastly, if you're going to ask and self answer, please make sure the questions are actually good and not just vehicles for the answer you really want to write :).
We're very happy to get coverage of small RPGs and as a contributer you qualify as an expert in Legend which is what we're here for.
So please, join our merry band, take a look at other questions too, vote as you see fit, maybe answer a few. Self-answered Q&As are acceptable, but make sure they’re legitimately questions that real users might ask. In fact, the best way to handle it may be to point to your fans that this resource exists, and is a place where you’re answering questions—if they have actual questions for you, and you answer them, then those will make great answers and should be fairly well-received.
(Though don’t have your fans spam the site with every question they can think of just to give you an excuse to promote the game more—that would be very poorly received.)